Problem: Simplify the following expression: $q = \dfrac{55y^3 - 22y^2}{-110y^3 - 88y^2}$ You can assume $y \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $55y^3 - 22y^2 = (5\cdot11 \cdot y \cdot y \cdot y) - (2\cdot11 \cdot y \cdot y)$ The denominator can be factored: $-110y^3 - 88y^2 = - (2\cdot5\cdot11 \cdot y \cdot y \cdot y) - (2\cdot2\cdot2\cdot11 \cdot y \cdot y)$ The greatest common factor of all the terms is $11y^2$ Factoring out $11y^2$ gives us: $q = \dfrac{(11y^2)(5y - 2)}{(11y^2)(-10y - 8)}$ Dividing both the numerator and denominator by $11y^2$ gives: $q = \dfrac{5y - 2}{-10y - 8}$